Let X be a complexe analytic manifolds and T*X its cotangent bundle. Let M be a coherent module over the ring of formal microdifferential operators on X. When the support (or characteristic variety) of M is a hypersurface, B. Malgrange has proved that we can decompose M in elementary systems at a generic point and after tensorization by the ring of microdifferential operators of q-fractionary order, for an appropriate integer q.

In this work, we generalize the above result: first for any not holonomic system and then for the holonomic systems.